On a crisp January afternoon in South London's Henry Wood Hall, an orchestra is rehearsing. Nothing unusual about that - this converted church has been a major rehearsal venue for 30 years - except for the people they're playing with. The double bass player picks out an ominous bassline, the percussionist strikes up a fractured rhythm and the two violinists join in with a choppy melody, but the star of the show is a wiry 23-year-old east London rapper called Bruza.

As the music becomes increasingly elaborate, Bruza rattles off witty observations about life in the capital. The song is called In the Endz. During the last verse, he gets his words mixed up and sputters to a halt, twisting his arm behind his head in a gesture of frustration. "Shit," he says to the orchestra. "Sorry, people. We'll get there in the end." There's a ripple of laughter and conductor Jason Yarde leads everyone through the song again. This time it goes perfectly. As Bruza leaves the rehearsal area, the orchestra give him a round of applause.

At the back of the room, the other MCs practice their parts under their breath, weaving and feinting like shadowboxers. One of the violinists, meanwhile, kills time between parts by knitting. "She shows her skills, man," Bruza says admiringly. "Her concentration levels are very good. I couldn't do that."

This unprecedented confluence of rapping and knitting is the fourth rehearsal for Urban Classic, a project that brings together the BBC Concert Orchestra (the full line-up will feature 36 musicians), four MCs (Bruza, Tor, Pase and Purple) and one beatboxer, Faith SFX. It will culminate in a performance at east London's Hackney Empire, broadcast on both Radio 3 and urban specialist radio station 1Xtra.

Urban Classic is the brainchild of Bigga Fish, a non-profit organisation that holds music workshops for schools, youth groups and young offenders institutes. "It came out of a conversation," explains general manager Genevieve Dowokpor. "'Wouldn't it be great to see urban artists with an orchestra?' It's one of those wacky ideas that a lot of people didn't want to touch. We were saying this is something we want to do and they were like, 'Yeah but how?'"

They found a sympathetic ear in Charles Hazlewood, the BBC Concert Orchestra's principal guest conductor. A fan of hip-hop since he first heard the Fugees 10 years ago, he has an appetite for unusual projects. The Concert Orchestra itself is no stranger to pop music. It recently backed Richard Ashcroft at a concert to launch his current album, and its freshly appointed composer in association is Radiohead's Jonny Greenwood.

Urban Classic is, however, a risky enterprise. As Hazlewood observes, "the territory of classical crossover is littered with bones of failed projects." Even at its best, it has been lopsided: classical outfits such as the Balanescu Quartet delving into pop's canon, or artists such as Kanye West fleshing out their sound with orchestras. At its worst, it has been a self-important attempt by self-important rock artists such as Rick Wakeman and Emerson, Lake & Palmer to don the mantle of "high art". Then there's the grim spectre of the anodyne classical pop peddled by the likes of Il Divo. "If anyone thought this was one of those soppy, saccharine classical pop crossovers I'd want to kill myself," Hazlewood says flatly.

What makes Urban Classic work is its unusual rigour. The electronic loops and samples of grime tracks have been painstakingly reconstructed using orchestral instrumentation by jazz saxophonist and composer Jason Yarde and grime producer DaVinChe; the genres are intertwined from the ground up. In the process, the songs have become more inventive: the programmed beat for In the Endz has been deconstructed into parts for three percussionists and the arrangements have become more adventurous. Dr Dre's Still DRE becomes a dramatic instrumental built around a harp and Faith SFX's beatboxing. "Classical musicians get bored just playing loops so we have to keep it interesting for them," says Yarde.

It's remarkable how well it all works. It's not perfect - the finale featuring all the MCs is a bit of a racket - but the rigour and intelligence of the arrangements creates a fusion, rather than a clash, of cultures. The most marked difference between the two groups of performers is social rather than musical: most of the MCs are young and black; most of the players are middle-aged and all are white. Yarde and Hazlewood both lament the lack of investment in introducing black youths to classical music. By contrast, grime is the perfect DIY medium. Someone with limited funds is far more likely to invest in a software programme and a microphone than a tuba. To the average grime MC, classical music is an alien culture from another Britain.

"They're two groups of people from two walks of life that don't normally have the opportunity to interact," says DaVinChe, a classically trained pianist. "When we first started working with the musicians a couple of the MCs were like, 'I feel like I'm in school with all my teachers around.'" As the rehearsals progressed, the gap shrank. "The double bass player asked me if I could explain the difference between grime, hip-hop and garage so we had a long discussion about that."

Cultural differences have, however, created more practical problems. Orchestras adhere to rigid schedules whereas MCs tend to run on what is known as "hip-hop time". Yarde admits that the initial workshop in December was hampered by certain MCs (he tactfully doesn't mention any names) turning up several hours late. At the Henry Wood Hall rehearsal, the orchestra members put down their instruments at 5.30pm because of other commitments. Some of the sheet music has only just arrived and Yarde and the MCs want to continue rehearsing, but they have to concede defeat.

"The scene that I've been around, people ain't too punctual," admits Bruza, whose real name is Sean Barker. "I can record until silly hours of the morning, but obviously these people have got places to be. The musicians are very professional, which is only going to rub off on us."

Bruza, who had never previously listened to classical music, has had his appetite whetted. Likewise, the orchestra members have been introduced to Britain's most fertile urban music.

Hazlewood is realistic about Urban Classic's impact - "I don't expect any grime fans to rush off and buy the Ring Cycle" - but he is convinced it will surprise people. DaVinChe, meanwhile, hopes it will advertise grime's versatility. It is a challenging time for a genre tipped to crash the charts since Dizzee Rascal's debut in 2003 yet still unable to make a significant commercial impact despite the wealth of talent available. "It is frustrating for the artists because they know they're making good music and when people do listen to the music they love it and want to hear more," says DaVinChe. "But it's getting people to have that first listen."

One solution could be musical miscegenation. Hip-hop elbowed its way on to mainstream radio playlists when Run-DMC hooked up with Aerosmith for Walk This Way in 1986, and something similar might work for grime. "This can only benefit the music as a whole," concludes Bruza. "As long as these things are happening it shows people that grime is a universal music. People of all kinds of backgrounds can link up. You can forget about where you're from and what situation you're living in and think, 'Well, we like the same kind of music.' Before I wouldn't have been into classical music but now I'm in it, man. Learning as I go along."

· Urban Classic is at the Hackney Empire, London E8, on Thursday. Box office: 020-8985 2424. It will be broadcast live on Radio 3 and 1Xtra.